Back a couple weeks ago I applied for a new credit card. When I returned from my vacation (yes I was gone last week--didja notice?

) I had a letter from them saying they were rejecting me because they couldn't verify the information on my application. Since I've got excellent credit, I didn't figure they'd be turning me down for anything but a paperwork screwup, so I called them up to see what the issue was. I talked to a woman who sounded like she could barely be bothered to help me, and she told me that when they ran my social security number a different name came back. She said if I could get a letter from the Social Security Administration and a current pay stub they'd look at it again.
Needless to say this didn't thrill me. I was thinking about what I ought to do to deal with this and it occured to me I should try to find out where they got this information from (one of the credit bureaus? Which one?). So I called them back and spoke to a different woman. She was not so rude and before I could even explain why I had called she started asking me some stuff to verify things, and had some brief trouble confirming the name of my employer. (Among other issues, there's another institution with a similar name in a different area code.) At this point she said OK we have what we need, we had to straighten out the business with your employer--we'll get back to you. So I told her what the first woman said, and she said no, there was no problem with my SSN everything was just fine.
OK, so now I have to figure out whether there's really a problem here with somebody else's name attached to my SSN? Which call center employee do I believe? Any advice for tracking this down definitively?